Low-speed fan noise mainly features dipole sound radiation. For such a fan operating in a duct, the low- to medium-frequency radiation derives mainly from the unsteady, axial forces acting on the rotating blades. Recently, we have found, both theoretically and experimentally, that self-cancellation of sound can be achieved by placing the dipole in an expanded segment of the duct which provides a reverberating environment with a reduced radiation impedance. The insertion loss spectrum shows a very broadband appearance similar to but is better than the transmission loss spectrum of an expansion chamber silencers used for reflecting an incident plane wave. Parametric analysis reveals that the expansion ratio controls the peak insertion loss, while the chamber length controls the single-lobe bandwidth. Simple plane wave analysis implies that short chamber would give wider stopband with a chamber of vanishing length yielding the best result. It is shown here that such analysis fails when the chamber is too short. For a given finite frequency band, there exists an optimal chamber length. Spectral element analysis reveals details of such optimal length and the result is explained in terms of the known fundamentals of dipole radiation and duct acoustics.